This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166143 #39 May 02 2025 18:46:13
%S A166143 1,13,31,55,85,121,163,211,265,325,391,463,541,625,715,811,913,1021,
%T A166143 1135,1255,1381,1513,1651,1795,1945,2101,2263,2431,2605,2785,2971,
%U A166143 3163,3361,3565,3775,3991,4213,4441,4675,4915,5161,5413,5671,5935,6205
%N A166143 a(n) = 3*n^2 + 3*n - 5.
%H A166143 Vincenzo Librandi, <a href="/A166143/b166143.txt">Table of n, a(n) for n = 1..5000</a>
%H A166143 Leo Tavares, <a href="/A166143/a166143.jpg">Illustration: Truncated Point Hexagons</a>
%H A166143 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A166143 a(n) = a(n-1)+6*n, a(1)=1.
%F A166143 From _G. C. Greubel_, Apr 26 2016: (Start)
%F A166143 G.f.: (5 - 16*x + 5*x^2)/(-1 + x)^3.
%F A166143 E.g.f.: (-5 + 6*x + 3*x^2)*exp(x).
%F A166143 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A166143 a(n) = A003215(n) - 6. - _Leo Tavares_, Jul 05 2021
%F A166143 Sum_{n>=0} 1/a(n) = Pi*tan(sqrt(23/3)*Pi/2)/sqrt(69). - _Vaclav Kotesovec_, Jul 06 2021
%t A166143 LinearRecurrence[{3,-3,1}, {1,13,31}, 50] (* _G. C. Greubel_, Apr 26 2016 *)
%t A166143 Table[3 n^2 + 3 n - 5, {n, 45}] (* or *)
%t A166143 Rest@ CoefficientList[Series[(5 - 16 x + 5 x^2)/(-1 + x)^3, {x, 0, 45}], x] (* _Michael De Vlieger_, Apr 27 2016 *)
%o A166143 (Magma) [-5+3*n^2+3*n: n in [1..50]];
%o A166143 (PARI) a(n)=3*n*(n+1)-5 \\ _Charles R Greathouse IV_, Jan 11 2012
%Y A166143 Cf. A003215.
%K A166143 nonn,easy
%O A166143 1,2
%A A166143 _Vincenzo Librandi_, Oct 08 2009
%E A166143 New name from _Charles R Greathouse IV_, Jan 11 2012